SACRAMENTO (AP) — The agency overseeing California’s health insurance exchange offered a bit of breathing room for consumers who tried but failed to meet Monday’s deadline for coverage starting in the new year, as its website and call centers were overwhelmed by last-minute demand.

It did not formally extend the sign-up deadline beyond Monday, as the Obama administration did for the 36 states using the federal health insurance exchange. But as high volume threatened to undermine the deadline-day attempts of thousands of consumers, the agency offered help for people who were trying to enroll.

Executive Director Peter Lee told reporters that Covered California will institute a “grace period” for those who attempted to get coverage Monday but were unable to sign up.

“We’re gonna help people get across the finish line,” he said. “…People that have started the application today, we’re gonna get across. If for some reason, through no fault of their own, they tried to start an application today, we’re gonna take that on a case-by-case basis.”

Lee did not commit to a date when that grace period would end but said the agency’s goal was to have an insurance policy in place for everyone who “made a good faith effort” to get one by Monday’s deadline.

“We need to know you tried,” he said.

Monday was the deadline to sign up for coverage so insurance policies will be in place by Jan. 1, and consumers have until Jan. 6 to pay their premiums.

Covered California has had a surge in the number of people signing up for coverage as the deadline approached. Lee said preliminary data show the number people who had signed up for an individual health insurance policy through California’s state-run exchange had topped 400,000. The previously reported figure was 109,000 by the end of November.

About two-thirds of those who have signed up so far are eligible to receive a federal subsidy that will help lower their monthly premiums, while about one-third make too much money for a subsidy, Lee said.

The need for Covered California to provide consumers some wiggle room became evident as Monday wore on, with complaints surfacing from people who were attempting to sign up for an insurance plan but were unable to do so.

Gene Nelson, an adjunct professor in the biomedical engineering department at Cal Poly San Luis Obispo, had been frustrated in his attempts to apply through the website and through Covered California’s call centers.

He faced a variety of challenges on the website, including stalls, time-outs and messages warning of invalid user names and passwords that left him unable to even create an account.

When he contacted the call center for help, a recorded message told him to sign up through the website instead and then bounced him off the telephone call with a series of busy-signal beeps. He said he was not given the option to hold on the line for an available operator.

“It’s impossible,” he said.

Nelson, who will be 62 in January, said he had been without health insurance since 2009 and is trying to get coverage for him and his wife. He has not been called back this year to teach courses at Cal Poly and was not provided health insurance by the university even when he did teach last year.

He was skeptical about Covered California’s offer of a grace period for those who were unsuccessful in signing up for coverage Monday.

“But that’s predicated upon, among other things, getting the first step done so that I can apply. But I can’t get the first step done, so I don’t think it would apply,” said Nelson, who has a doctorate degree in natural sciences. “And I’m sure there will be a lot of people like me.”

When a reporter for The Associated Press tried the website late Monday afternoon, a click on the “Apply Now” button led to a 25-second delay and ended with a message that read, “Sorry, An Error Has Occurred In the System. Please contact System Administrator.”

While Monday was the deadline to sign up for an individual policy that will start in the new year, consumers will have until the end of March to buy coverage and avoid the federal tax penalty under the federal health reform law. Policies purchased by the 15th of each month will start the first day of the following month.

Despite occasional problems with California’s rollout of the Affordable Care Act, health insurance companies are generally pleased with how the marketplace is operating in the state, said Patrick Johnston, chief executive of the California Association of Health Plans, which represents insurers.

He described the level of consumer interest in signing up for health care policies as enormous and said insurance companies had responded by increasing staff and boosting their outreach to private insurance brokers.

“The surge is a challenge, but health plans are meeting it,” Johnston said Monday.

So far, enrollment has skewed toward older people. That could cause financial problems for insurers if the pool becomes heavily weighted toward those who require more medical care and does not include enough younger and healthier people.

In response, Covered California has been ramping up its marketing efforts to the younger demographic.